The Hammers left Upton Park at the end of last season to move to the stadium which hosted athletics at the London 2012 Olympics.
The kick-off at their new venue comes as they look to overcome a first-leg deficit to beat their Slovenian opponents and advance to the play-off round of the Europa League.
Fifty-four-thousand fans will witness history as West Ham start their new era, but the official stadium opening will not take place until Sunday's marquee friendly against Juventus, and Bilic conceded it may still feel like an away game for now.
"It doesn't feel like a home game," he said.
"We will do the same things - go for a meal, get on the coach, but instead of Upton Park, we'll be coming here in front of 54,000.
"There's no better way to adjust to a new stadium than playing in it and hopefully we are going to start tomorrow."
A disappointing display saw an experienced West Ham XI beaten 2-1 in Slovenia last week, with those players who missed the trip likely to sit out again on Thursday.
Dimitri Payet, Angelo Ogbonna and James Collins will not take part after their international exertions at Euro 2016 while Aaron Cresswell is out with a knee injury, as is Manuel Lanzini who was injured on international duty with Argentina ahead of the Olympics.
But Bilic still wants to progress, even if he feels the fitness advantage of Domzale - whose domestic season is already under way - could help West Ham's opponents.
"It's a qualification game in a competition we want to qualify for
It's the first game at our new stadium so it's a big game for us," he said.
"If we play much better than we did in the first leg, we have a really great chance to go through
We have good players to do that.
"Domzale have had a few more competitive games than us, but if a team is braver, more hungry, then these things happen.
"We are going to have to play much better than the first leg
We don't have a mountain to climb, but a job to do."
Bilic would not be drawn on new arrivals despite the club being linked with a new left-back given Cresswell's knee problem.
Both Davide Santon of Inter Milan and Norwich's Martin Olsson are reported targets but Bilic remained coy.
"Even before Cresswell got injured, we were looking to strengthen at left-back," he said.
"He's a very good player, but we were looking for backup
We are not the only team looking for a left-back, and it's hard to find a good one we like and who is willing to come
It's now a priority."
Bilic did confirm striker Diafra Sakho's potential move to West Brom could be close to completion, as could the arrival of Sao Paulo forward Jonathan Calleri on a season-long loan.
Source : PA
Source: PA